System and method for multi-sampling primitives to reduce aliasing

ABSTRACT

A method and system for performing multi-sample, antialiased rendering of images by performing multi-sample antialiasing at the primitive level. Geometric primitives used to represent a graphics environment are set-up, and then shifted by a sub-pixel offset and rendered to generate values for pixels of an intermediate image. The shifting and rendering is repeated for the geometric primitive, each time generating values for pixels of another intermediate image. The values for the pixels of the intermediate images are combined to produce values for the respective pixels of the resulting image.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of pending U.S. patent applicationSer. No. 11/417,387 filed May 3, 2006, which is a continuation of U.S.patent application Ser. No. 09/945,367 filed Aug. 31, 2001 and issued asU.S. Pat. No. 7,145,577 B2 on Dec. 5, 2006. These applications andpatents are each incorporated herein by reference.

TECHNICAL FIELD

The present invention is related generally to the field of sampledimagery, and more particularly, to systems and methods for generatingantialiased, sampled images.

BACKGROUND OF THE INVENTION

In computer graphics, a sampled image is created from input geometry ormathematical computations that typically represent a scene. The sampledtwo-dimensional (2D) image is represented by an array of discrete unitsreferred to as pixels. The pixels are generally arranged along twoperpendicular axes corresponding to the horizontal and vertical axes ofthe image. The color or monochrome values of the pixels are determinedby calculated sample values, typically derived from scene data, lightingdata, or other input data. The image represented by the array of pixelsis typically transferred to a visual medium, such as by being printedonto paper or film, or displayed upon a computer display device. Thenumber of pixels and number of colors or values used in rendering agraphics image limit, to some extent, the visual qualities andcharacteristics of the viewed image, for example, the image definition,smoothness, and detail. Consequently, a great amount of effort has beendevoted to developing sophisticated graphics processing and renderingtechniques for higher image quality.

In addition to high-quality static images, high-quality animationdepicting visual effects of motion, is also desirable. The illusion ofmotion is created by quickly displaying related images in a sequence ofimage frames in which an object appears in different positions. Althoughthe motion of the object may appear to be continuous, each frame of theanimation is a separate image that is displayed momentarily. Thus, thequality of each frame will affect the quality of the animation or theillusion of motion. Depending upon the rendering algorithm, representingmotion may result in the creation of motion artifacts. The morenoticeable effects include static edge-effects such as “staircasing,” aswell as “crawling” and “popping” of pixels on an edge of a moving objecthaving a value that contrasts against a background having a differentvalue.

For example, consider an object having a straight edge and of a firstcolor which appears to be moving across a background of a second color.As the edge of the object moves across a pixel, there must be adetermination as to when the color of the pixel changes from the colorof the background to the color of the object. If a single samplelocation within the pixel is taken to determine its color, then, whenthe edge of the object passes the single sampling location, the color ofthe pixel is changed. The location of a single sample location istypically located at the center of the pixel, and thus, the value of thepixel is determined by the value calculated for the center of the pixel.As a result of a single sample point determination, the edge of anobject may extend well into the region represented by the pixel, butbecause the edge has not reached the center (i.e., the sample point) ofthe pixel, the pixel may continue to have the color of the background.As a result, when multiple images or frames are displayed in sequence toprovide the illusion of objects in motion, pixels along the edge of anobject may “pop” from one color or value to another. This effect can bedistracting for a viewer. The relative motion of an object with respectto the orientation of the pixels of the image may be such that pixelsalong the edge of the object pop values in a manner and with aregularity that creates a visual effect of the edge of the object“crawling.”

There have been many different approaches to addressing the issue ofaliasing. One such approach is to increase the resolution, or the numberof pixels used to represent an image. Although the available resolutionof computer graphics displays and computer printing devices have reducedaliasing, there are practical limitations on the manufacture of displaysand other devices used for forming or recording an image which willlimit the maximum available resolution. Moreover, no matter how high a(finite) resolution is used to represent a graphics image, so long asthe value of each pixel is only approximated from calculated values fordiscrete, sample points, within the pixel, the image is subject to somedegree of aliasing, and a sequence of such images is subject to motionartifacts.

In another approach, aliasing can be “antialiased” to some degree bycalculating multiple number of values in determining a final value foreach pixel. That is, multi-sampling systems for antialiased renderinguse sample values from multiple samples taken from a pixel region indetermining the value of the respective pixel. For example, whenmulti-sampling is applied to the previous example, as the edge of theobject passes the first of the sample locations in a pixel region, thepixel is given a value that is a compromise between the value of theobject and the disparate value of the background. Where the size, shapeand motion of the object result in the object gradually and completelycovering the pixel, the value of the pixel will change each time theobject covers another sample location until all of the sample pointsshare the color of the object, at which time the pixel takes on thecolor of the object.

One approach to implementing the previously described antialiasingtechnique has been to shift the input geometry of the entirethree-dimensional (3D) environment a sub-pixel distance for each of thesub-pixel sample locations and then repeat the entire rendering orrasterization process. In effect, the rendering process, from generatingscene geometry through rasterizing the scene, is repeated for thecalculation of each of the multiple samples. Although the resultingimage is antialiased, this approach consumes considerable processingresources of a graphics processing system because multiple passesthrough the process of generating the scene geometry are needed. Thetime necessary to generate the multiple frames is a linear function ofthe number of desired samples, and as a result, no economy of scaleperformance gains would typically be realized. Moreover, the generatingthe geometry of the 3D environment multiple times necessitates eitherapplication driven generation of the frames, or an arbitrary amount ofbuffering within the graphics processing system to store the resultingdata for an arbitrarily complex scene.

Therefore, there is a need for an alternative system and method forrendering an image from a representation of a scene, while reducingaliasing, such as motion artifacts and edge effects.

SUMMARY OF THE INVENTION

The present invention relates to a method and system for performingmulti-sample, antialiased rendering of images by performing multi-sampleantialiasing at the primitive level. Values for pixels of an image of anenvironment represented by geometric primitives are calculated by thesystem. Geometric data is used to represent the geometric primitives,which are set-up into a scene of the environment. A geometric primitiveof the scene is shifted by a sub-pixel offset and rendered to generatevalues for pixels of an intermediate image. The shifting and renderingis repeated for the geometric primitive, each time with the valuesgenerated at the respective location stored to a buffer. The storedvalues for the pixels of the intermediate images are combined to producevalues for the respective pixels of the resulting image.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow diagram for conventional graphics pipelined processing.

FIGS. 2 a and 2 b are a flow diagram for graphics processing accordingto aspects of the present invention.

FIG. 3 is a diagram of a multi-sample pattern according to anotherembodiment of the present invention.

FIG. 4 is a block diagram of a graphics processing system according toan embodiment of the present invention.

FIG. 5 is a block diagram of a computer system including the graphicsprocessing system of FIG. 4.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the present invention render antialiased images byreducing artifacts in both static images and also in motion pictures oranimation. The systems and methods described herein perform antialiasedrendering through a process of taking multiple samples, or“over-sampling” at the primitive or primitive set level for calculatingthe colors or values of pixels forming a resulting computer graphicsimage. Certain details are set forth below to provide a sufficientunderstanding of the invention. However, it will be clear to one skilledin the art that the invention may be practiced without these particulardetails. In other instances, well-known circuits, control signals,timing protocols, and software operations have not been shown in detailin order to avoid unnecessarily obscuring the invention.

Illustrated in FIG. 1 is a process flow diagram 100 of a conventional 3Dgraphics pipeline process. It will be appreciated that FIG. 1 does notnecessarily represent a physical model of a graphics pipeline since thestages illustrated can be implemented in either software or hardware.Graphics information stored in a database is provided to the graphicspipeline (step 104) to begin construction of the 3D environment. Thetype of geometric data typically included in the database definevertices of geometric primitives having surfaces that are used constructthe 3D objects, as well as attributes of the respective primitives, suchas surface color, normal vector information, specular value, and thelike. Along with the geometric data, environmental information is alsostored. Environmental information includes such data as the number,color, and location of illumination sources, atmospheric properties, andthe like.

The geometric data is typically provided to the graphics pipelineprocess in an object coordinate space and requires transformation into aworld coordinate space (step 108). Various conventional transformationtechniques are well known, and consequently, will not be discussed indetail herein. A viewpoint from which the 3D environment will be viewedis determined and a corresponding view volume is constructed. In orderto ease the processing burden, the primitives located outside of theview volume are rejected, and the primitives that are partly inside theview volume are clipped (step 112). Thus, only the primitivescontributing to the resulting image need to be processed through thegraphics pipeline.

Following the primitive clipping process, the vertices of the of theprimitives to be processed are transformed from the world space to ascreen coordinate space corresponding to the 2D representation of the 3Denvironment. The attributes for the primitives, such as for the surfacenormal vector for the surface of a primitive, are transformed to thescreen coordinate space as well (step 116). Additional steps to setupthe primitives take place after the transformation to the screen space(step 120), such as texture application. A rasterization or renderingstep is then performed which generates pixel attributes for eachprimitive (step 124). The pixel attribute data are typically written toa pixel buffer or frame buffer. The pixel attribute data stored in thebuffer are then used for constructing a resulting 2D image of the scene.Although embodiments of the present invention will be described hereinas being applied to 3D graphics, it will be appreciated that the presentinvention may be applied in performing antialiasing to 2D graphics aswell.

As mentioned previously, conventional approaches to antialiasing havebeen to either shift the geometry of the 3D environment a sub-pixeldistance for each sub-pixel sample locations, and repeat the entiregraphics pipeline process for each of the samples, or render a framemultiple times with the pixel values written into separate buffers. Forexample, where four sub-pixel samples are calculated for the attributesof a pixel, several of steps 104-124 of FIG. 1 are repeated four times,each time with an entire frame shifted to a different sub-pixelposition. The pixel attribute data resulting from each pass through thegraphics pipeline process are written to a different pixel buffer, andthen subsequently combined to determine final attributes of pixels forthe final image of the scene. However, as also mentioned previously, thetechnique of rendering a frame multiple times consumes considerableprocessing resources of a graphics processing system because it requiresfour passes through the process of generating the scene geometry. Thetime necessary to generate the multiple frames is a linear function ofthe number of desired samples, and as a result, no economy of scaleperformance gains would typically be realized. Moreover, the generatingthe geometry of the 3D environment multiple times necessitates eitherapplication driven generation of the frames, or an arbitrary amount ofbuffering within the graphics processing system to store the resultingdata for an arbitrarily complex scene.

In contrast to the conventional approach, embodiments of the presentinvention reduce the impact a multi-sample antialiasing operation has onprocessing overhead by performing multi-sampling at the primitive level.That is, rather than rendering an entire frame multiple times, it is thegeometric primitives themselves that are rendered multiple times. As aresult, only the drawing operation for each of the primitives isrepeated for each of the sub-pixel samples, rather than repeatingmultiple passes through the process of generating the geometry for themultiple scenes. Additionally, cache mechanisms already operating withina graphics pipeline, for example, texture caching, permits rapidrendering of the multiple instances of the primitive.

Illustrated in FIGS. 2 a and 2 b are a process flow diagram 200 of anembodiment of the present invention. It will be appreciated that theprocess flow 200 of FIGS. 2 a and 2 b is provided as an example toillustrate aspects of the present invention. Consequently, particularsteps as described below may be removed or reorganized without departingfrom the scope of the present invention.

Steps 204-220 of the process flow are conventional and are similar tosteps 104-120 of FIG. 1. However, at step 224, the primitive that is tobe rasterized is shifted by a sub-pixel amount prior to rasterization(step 224). The primitive is shifted to a position corresponding to thelocation of one of the sub-pixel samples and then rasterized and theresulting sample values are written to a pixel buffer (step 228). Theprocess of shifting the primitive, rasterizing and writing the resultingsample values to a buffer is repeated for each of the sub-pixel samplelocations or until the appropriate number of samples are taken for apixel (steps 232-240). The rasterization or rendering of the shiftedprimitive can be typically implemented using conventional circuitry andprocessing commands. For example, the triangle engine could beinstructed to draw each primitive multiple times by reissuing a drawcommand, each time shifting one of the vertices of the primitive asub-pixel offset plus a memory buffer offset, and then re-rendering theprimitive. The shifting and rendering process is performed at theprimitive level until all of the primitives of the scene are rendered(steps 244-246).

The sample values in the respective buffers are then combined to producefinal values for pixels of the image (step 248). Many well-knownconventional blending or combining techniques can be used for thepresent invention. In one embodiment, the sample values from each of thedifferent buffers for a respective pixel are averaged together. That is,each of the sample values contribute equally to the final value of thepixel, such as in a simple box filter. In another embodiment, the samplevalues are weighted as a function of the respective offset distancesfrom the center of the pixel. For example, sample values calculated atsub-pixel sample locations located at greater distances from the pixelcenter will contribute less to the final value of the pixel than thosecalculated at sample locations closer to the pixel center. For example,a Gaussian weighting function can be used.

In an alternative embodiment, sets of primitives, such as a tristrip,are re-rendered instead of an individual primitive. It will beappreciated that other known collections of geometric primitives can beused as well without departing from the scope of the present invention,such as triangle fans, sets of disjoint triangles, and the like. In theembodiment where the set of primitives is a tristrip, the tristripdefinition should be buffered so that it may be reissued multiple times.However, it may be the case that the buffers of the graphics pipeline isinsufficient to buffer enough geometric state for more than only a fewtriangles. Thus, consideration of the available pipeline resourcesshould be considered when implementing this embodiment.

In alternative embodiments of the present invention, the use ofrendering buffers can be economized. For example, with some loss ofsampling accuracy, n instances of pixel color buffers and one z-buffercould be utilized. That is, for the n−1 issues of the primitive, writingto the z-buffer is inhibited. However, the nth issue of the primitive isrendered with the z-buffer inhibit removed. Thus, only one z-buffer isrequired for implementing the present invention. It will be appreciatedthat embodiments of the present invention may be implemented using otherbuffers whose state affects the rendering process, and which can bemodified as part of the rendering process.

FIG. 3 illustrates an example of a sampling pattern 300 that can be usedin embodiments of the present invention. A pixel region 300 is shownwith sampling locations 304 and 308. The pixel region 300 represents theregion that a pixel of the resulting image covers. As shown in FIG. 3,the pixel region 300 is dividend into four equal sub-regions. Thesampling locations 304 and 308 are positioned at the center of theupper-left sub-region and the lower-right sub-region. Note that thesampling locations 304 and 308 are offset from a center 312 of the pixelregion 300 by sub-pixel offsets d₁ and d₂, respectively. Shifting ageometric primitive by the offset d₁ will effectively result in a samplebeing calculated at the sampling location 304. Similarly, shifting thegeometric primitive by the offset d₂ will effectively result in a samplebeing calculated at the sampling location 308. Thus, by shifting thegeometric primitive by the respective offsets, multiple samples for apixel may be calculated and then used for antialiasing.

The sampling pattern 300 may be repeated for each of the pixels duringthe rendering of the primitive by selecting offsets that shift theprimitive to a location that corresponds to the sampling locations ofthe sampling pattern 300. Alternatively, the sampling pattern 300 can beused as a basis from which dynamic offsets could be determinedstochastically to implement “jittered” antialiasing. Both embodimentscan be implemented using well-known conventional techniques. Furtherexamples of the different types of sampling patterns and techniques aredescribed in more detail in co-pending U.S. patent application Ser. No.09/823,935, entitled MULTI-SAMPLE METHOD AND SYSTEM FOR RENDERINGANTIALIASED IMAGES, to Peterson et al., filed Mar. 30, 2001, which isincorporated herein by reference. It will be appreciated, however, thatmany different sampling patterns could be used in embodiments of thepresent invention in addition to those described herein and in theaforementioned co-pending patent application. Therefore, the scope ofthe present invention should not be limited by the particular samplingpattern employed, except to the extent the limitation is recited in oneof the claims attached hereto.

FIG. 4 illustrates circuitry included within the graphics processingsystem 400 for performing various graphics and video functions,including antialiasing according to embodiments of the presentinvention. In the following description, the various stages of thegraphics processing system 400 will be described as performing variousfunctions and graphics processes. However, the various functions andgraphics processes may also be performed by or associated with adifferent stage than described herein. Consequently, it will beappreciated that the particular embodiment of the graphics processingsystem 400 is provided merely as an example, and is not intended tolimit the scope of the present invention.

As shown in FIG. 4, a bus interface 402 couples the graphics processingsystem 400 to the expansion bus 434 or optionally a high-speed bus 436.In the case where the graphics processing system 400 is coupled throughthe high-speed data bus 436, the bus interface 402 will include a DMAcontroller (not shown) to coordinate transfer of data to and from thegraphics processing system 400. A graphics processor 404 is coupled tothe bus interface 402 and is designed to perform various graphics andvideo processing functions, such as, but not limited to, generatingvertex data and performing vertex transformations for polygon graphicsprimitives that are used to model 3D objects. The graphics processor 404is coupled to a triangle engine 408 that includes circuitry forperforming various graphics functions, such as attributetransformations, rendering of graphics primitives, and generatingtexture coordinates for a texture map. The circuitry of the triangleengine 408 can also be used to perform antialiasing in accordance withembodiments of the present invention by over-sampling within the pixelsof the graphics image to reduce aliasing artifacts.

A pixel engine 412 is coupled to receive the graphics data generated bythe triangle engine 408. The pixel engine 412 contains circuitry forperforming various graphics functions, such as, but not limited to,texture application or mapping, bilinear filtering, fog, blending, andcolor space conversion. A memory controller 416 coupled to the pixelengine 412 and the graphics processor 404 handles memory requests to andfrom a local memory 420. The local memory 420 stores graphics data, suchas pixel values. A display controller 424 is coupled to the memorycontroller 416 to receive processed values for pixels that are to bedisplayed. The output values from the display controller 424 aresubsequently provided to a display driver 432 that includes circuitry toprovide digital signals, or convert digital signals to analog signals,to drive a display device (not shown).

It will be appreciated that additional processes and circuitry that havenot been shown or described with respect to FIG. 4 may also be includedin the graphics processing system 400. For example, various data buffersused throughout the graphics processing operation, such as a pixelbuffer, a z-buffer, and stencil buffer, are included in the differentfunctional blocks of the graphics processing system 400. However, theyhave not been discussed in detail in order to avoid unnecessarilyobscuring the invention. It will be further appreciated that thecircuitry included in the functional blocks of the graphics processingsystem 400 are conventional in design and are well understood by thoseof ordinary skill in the art. Consequently, the description providedherein is sufficient to enable the same to practice embodiments of thepresent invention.

As previously mentioned, the graphics processing system 400 facilitatesantialiasing by over-sampling for at least some pixels of a graphicsimage. The sample values for the multiple samples for a pixel arecalculated for each triangle, or other primitive, covering, or partiallycovering, the pixel. Calculation of the multiple sample values occurs atthe primitive or primitive set level to avoid repeating many of theprocessing intensive steps of generating the geometry of the 3Denvironment. Each primitive is shifted by a sub-pixel offset andrasterized for the multiple samples. The sample value for a given sampleposition within a given pixel may be then stored or altered, forexample, by well-known z-buffer techniques, in accordance with theprocessing of other data, such as other primitives touching the samesample position in the same pixel. In one embodiment, the final samplevalues for a given pixel are subsequently combined in the pixel engine412 or texture engine (not shown) or blend unit (not shown), todetermine a sample value for the pixel in the resulting image.

Although the antialiasing operation has been described as beingimplemented in the triangle engine 408, it will be appreciated that theantialiasing operation may also be implemented in circuitry that isseparate from the triangle engine 408, or included in one of theaforementioned circuit blocks of the graphics processing system 400,such as the pixel engine 412. Alternatively, the antialiasing operationmay be divided and carried out by various circuit blocks of the graphicsprocessing system 400. For example, portions of the antialiasingoperation may be shared between the triangle engine 408 and the pixelengine 412. That is, when geometric primitives are rendered by thetriangle engine 408, sample values are calculated for each sample point,typically of each pixel having a portion covered by the geometricprimitive. Once the over-sampling is performed, the pixels may befurther processed, for example, for depth, texture, and the like, andthen the pixel engine 412 may perform the down-sampling or combining ofthe multiple sample values. Therefore, the particular implementation ofthe antialiasing circuitry 414 is a detail that may be modified withoutdeviating from the subject matter of the invention, and should not beused in limiting the scope of the present invention. Moreover,embodiments of the present invention may be implemented in software orhardware, or a combination thereof. Those of ordinary skill in the arthave sufficient understanding to implement the present invention assuch.

It will be appreciated that the sample values discussed herein mayrepresent values such as color values, grayscale values, depth values,and the like, at a sample location. It will be further appreciated thatthe sample values for the samples may consist of several differentcomponents. For example, a sample value may represent not only a pixelcolor, as a combination of red, green, and blue color components, butalso a depth value. Another example includes sample values representingpixel colors which are combinations of luma and chroma components.Consequently, because it is well understood in the art, althoughcircuitry to perform graphics operation for each of the components isnot expressly shown or described herein, embodiments of the presentinvention include circuitry, control signals, and the like necessary toperform operations on each component for multi-component sample values.

FIG. 5 illustrates a computer system 500 in which embodiments of thepresent invention are implemented. The computer system 500 includes aprocessor 504 coupled to a memory 508 through a memory/bus interface512. The memory/bus interface 512 is coupled to an expansion bus 516,such as an industry standard architecture (ISA) bus or a peripheralcomponent interconnect (PCI) bus. The computer system 500 also includesone or more input devices 520, such as a keypad or a mouse, coupled tothe processor 504 through the expansion bus 516 and the memory/businterface 512. The input devices 520 allow an operator or an electronicdevice to input data to the computer system 500. One or more outputdevices 524 are coupled to the processor 504 to receive output datagenerated by the processor 504. The output devices 524 are coupled tothe processor 504 through the expansion bus 516 and memory/bus interface512. Examples of output devices 524 include printers and a sound carddriving audio speakers. One or more data storage devices 528 are coupledto the processor 504 through the memory/bus interface 512 and theexpansion bus 516 to store data in, or retrieve data from, storage media(not shown). Examples of storage devices 528 and storage media includefixed disk drives, floppy disk drives, tape cassettes and compact-discread-only memory drives.

The computer system 500 further includes the graphics processing system400 (FIG. 4) coupled to the processor 504 through the expansion bus 516and memory/bus interface 512. Optionally, the graphics processing system400 may be coupled to the processor 504 and the memory 508 through othertypes of architectures. For example, the graphics processing system 400may be coupled through the memory/bus interface 512 and a high speed bus536, such as an accelerated graphics port (AGP), to provide the graphicsprocessing system 400 with direct memory access (DMA) to the memory 508.That is, the high speed bus 536 and memory bus interface 512 allow thegraphics processing system 400 to read and write memory 508 without theintervention of the processor 504. Thus, data may be transferred to, andfrom, the memory 508 at transfer rates much greater than over theexpansion bus 516. A display 540 is coupled to the graphics processingsystem 400 to display graphics images. The display 540 may be any typeof display, such as those commonly used for desktop computers, portablecomputers, and workstations, for example, a cathode ray tube (CRT), afield emission display (FED), a liquid crystal display (LCD), or thelike.

From the foregoing it will be appreciated that, although specificembodiments of the invention have been described herein for purposes ofillustration, various modifications may be made without deviating fromthe spirit and scope of the invention. Accordingly, the invention is notlimited except as by the appended claims.

1. A method for calculating pixel values, the method comprising:transforming geometric primitives from a first coordinate space to asecond coordinate space; and for each transformed primitive: renderingthe transformed primitive to generate at least one first sample valuefor a pixel; shifting the transformed primitive in the second coordinatespace by a respective sub-pixel offset; and rendering the shiftedtransformed primitive to generate at least one second sample value forthe pixel; and combining the first and second sample values to generatea pixel value for the pixel.
 2. The method of claim 1, furthercomprising writing the first sample value to a first buffer and writingthe second sample value to a second buffer.
 3. The method of claim 2wherein either the first or second buffer comprises a z-buffer.
 4. Themethod of claim 1 wherein at least one of the plurality of geometricprimitives comprises a strip of connected triangles.
 5. The method ofclaim 1 wherein at least one of the plurality of geometric primitivescomprises a fan shaped set of connected triangles.
 6. The method ofclaim 1 wherein at least one of the plurality of geometric primitivescomprises a set of disjoint triangles.
 7. The method of claim 1 whereinshifting each of the plurality of transformed primitives by therespective first sub-pixel offset comprises shifting each of theplurality of transformed primitives to a respective sub-pixel locationcorresponding to a first sampling location of a sampling pattern.
 8. Themethod of claim 1 wherein combining the first and second sample valuescomprises averaging the values for the respective first and second setsof pixels for each of the plurality of transformed primitives.
 9. Themethod of claim 1 wherein combining the first and second sample valuescomprises weighting the values for the respective first and secondsamples as a function of respective offsets and combining the weightedvalues.
 10. A graphics system for calculating pixel values, the systemcomprising: a set-up engine configured to receive geometric data andgenerate transformed geometric data therefrom, the transformed geometricdata representing a plurality of geometric primitives in a newcoordinate space; a rendering stage coupled to the set-up engine andconfigured to receive the transformed geometric data for at least onegeometric primitive, the rendering stage configured to calculate a firstsample value for a pixel at least partially covered by the geometricprimitive, and further configured to shift the geometric primitive arespective sub-pixel offset from a first pixel position, and calculate asecond sample value for the pixel, and further configured to combine thefirst and second sample values to generate a pixel value; and a buffercoupled to the rendering stage and configured to store the pixel value.11. The graphics system of claim 10 wherein the rendering stage isfurther configured to shift the geometric primitive to additionalsub-pixel offsets and calculate at least one respective sample value foreach location of a sampling pattern.
 12. The graphics system of claim11, further comprising additional buffers, each configured to store atleast one of the respective sample values, and the number of which isequal to one less than the number of sampling locations.
 13. Thegraphics system of claim 12, further comprising a combining circuitcoupled to the additional buffers and configured to combine the samplevalues to generate the pixel value.
 14. The graphics system of claim 13wherein the combining circuit is further configured to average therespective sample values.
 15. The graphics system of claim 13 whereinthe combining circuit is further configured to weight the respectivesample values as a function of the respective sub-pixel offsets andcombine the weighted values.
 16. The graphics system of claim 10 whereinthe rendering stage includes a primitive buffer for storing transformedgeometric data and the geometric primitive comprises a strip ofconnected triangles.
 17. The graphics system of claim 10 wherein therendering stage includes a primitive buffer for storing transformedgeometric data and the geometric primitive comprises a fan shaped set ofconnected triangles.
 18. The graphics system of claim 10 wherein therendering stage includes a primitive buffer for storing transformedgeometric data and the geometric primitive comprises a set of disjointtriangles.
 19. A method for determining values for pixels of an image,the method comprising: in a graphics processing system, shifting aposition of a geometric primitive in a screen coordinate space from afirst pixel position to positions corresponding to respective samplinglocations of a sampling pattern, the sampling locations being arespective sub-pixel offset from the first pixel position; rendering inthe graphics processing system the shifted geometric primitivepositioned at each of the sampling locations to generate sample valuesfor a respective set of pixels representing the shifted geometricprimitive positioned at the each of the plurality of sampling locations;and calculating values for a resultant set of pixels representing therendered geometric primitive positioned at the first pixel position withthe sample values for the respective sets of pixels generated for thegeometric primitive positioned at the plurality of sampling locations ofthe sampling pattern.
 20. The method of claim 19, further comprisingwriting the sample values for each respective set of pixels generatedfor the geometric primitive positioned at one of the plurality ofsampling locations to a respective buffer.
 21. The method of claim 20wherein writing to a respective buffer comprises writing to a z-bufferafter writing to a plurality of pixel color buffers.
 22. The method ofclaim 19 wherein the geometric primitive comprises a strip of connectedtriangles, a fan-shaped set of connected triangles, or a set of disjointtriangles.
 23. The method of claim 19 wherein calculating values for aresultant set of pixels representing the rendered geometric primitivepositioned at the first pixel position with the sample values for therespective sets of pixels generated for the geometric primitivepositioned at the plurality of sampling locations comprises averagingthe sample values for the respective sets of pixels.
 24. The method ofclaim 19 wherein calculating values for a resultant set of pixelsrepresenting the rendered geometric primitive positioned at the firstpixel position with the sample values for the respective sets of pixelsgenerated for the geometric primitive positioned at the plurality ofsampling locations comprises weighting the sample values for therespective sets of pixels as a function of the respective samplinglocations and combining the weighted sample values.